Numerical evaluation of beam models based on the modified couple stress theory

An error in the beam model proposed by Lam, Yang, Chong, Wang, & Tong (2003) for the modified couple stress theory is found and corrected, and then the corrected model is verified by the finite element analysis. In addition, various beam models based on the modified couple stress theory are classified according to their characteristics, and evaluated numerically by the finite element analysis using 2D and 3D continuum elements through elastic cantilever beam problems. The results show that the corrected beam model of Lam et al. is the best fit for plane strain beam problems, while none of the beam models are appropriate for general beams of similar width and thickness dimensions. The reason is confirmed by the energy term analysis which reveals that the kinematic assumptions applied to the beam models are inappropriate when the beam shape is general.